deletions | additions       diff --git a/emailpolgraslandmong.tex b/emailpolgraslandmong.tex  index 5c9fdb4..ee0639c 100644  --- a/emailpolgraslandmong.tex  +++ b/emailpolgraslandmong.tex 
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The Z axis is defined here as the laser beam axis, and the ultrasound probe is in the XZ plane, as illustrated by Figure \ref{Figure1}.  In this experiment, we used first a 4x8x8 cm$^3$ water-based phantom made from 5\% polyvinyl alcohol, 0.1 \% black graphite powder and 1\% salt. Three freezing/thawing cycles were applied \cite{fromageau2007estimation}. \cite{17375819}.  The laser beam was emitted by a Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France), which produced a 200 mJ, 5 mm in diameter Q-switched pulse at a central wavelength of 532 nm during 10 ns. The absorption of the laser beam by the medium led to a local increase of temperature. The resulting temperature distribution equation in a semi-infinite space with a boundary plane at $z=0$ is given by $\nabla^2 T - \frac{1}{\kappa} \frac{\partial T}{\partial t} = - \frac{A}{K}$, where $T$ is the temperature distribution, $A$ the heat produced per unit volume per unit time and $K$ and $\kappa$ are respectively the thermal conductivity and diffusivity \cite{ready2012effects}. 
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In both cases, the absorption of the laser by the phantom leads to a local displacement which can propagate as elastic wave in the medium. To observe the elastic wave, the medium was scanned with a 5 MHz ultrasonic probe made of 128 elements and a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was used in ultrafast mode \cite{bercoff2004supersonic}, acquiring 1000 ultrasound frames per second. Due to the presence of graphite particles, the medium presented a speckle pattern on the ultrasound image. Tracking the speckle spots with an optical flow technique (Lucas-Kanade method) allowed to compute one component of the displacement in the medium (``Z-displacement'' or ``Y-displacement''). The laser beam was triggered 10 ms after the beginning of the ultrasound acquisition.